Wednesday, September 19th, 2012
3:00pm - 4:00pm, in Science 2-062

Simon Lunagomez

Harvard University

Bayesian Inference from Non-Ignorable Network Sampling Designs

Abstract: Consider a population where subjects are susceptible to a disease (e.g. AIDS). The objective is to perform inferences on a population quantity (like the incidence of HIV on a high-risk subpopulation, e.g. intra-venous drug abusers) via sampling mechanisms based on a social network (link-tracing designs, RDS). We phrase this problem in terms of the framework proposed by Rubin (1976). A new notion of ignorability (graph-ignorability) is proposed for this context and it is proved that RDS is not graph-ignorable. We develop a general framework for making Bayesian inference on the population quantity that: models the uncertainty in the underlying social network using a random graph model, incorporates dependence among the individual responses according to the social network via a Markov Random Field, models the uncertainty regarding the sampling on the social network, and deals with the non-ignorability of the sampling design. The proposed framework is general in the sense that it allows a wide range of different specifications for the components of the model we just mentioned. Samples from the posterior distribution are obtained via Bayesian model averaging. Our model is compared with state of the art methods in simulation studies and it is applied to real data. Work with Edoardo Airoldi.